Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2023/imperative-programming/3/b/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2023 / Imperative programming / 3 / b / Solution by Codex 0 2026-10-25
Every operation requires . The queries have postconditions “return ” and “return ” respectively, leaving both functions unchanged. An incoming increment additionally requires and has
(1)
The outgoing increment analogously requires , increments only , and preserves . These frame conditions prevent an implementation from accidentally changing another user's count. Here a subscript zero denotes the old program state.
trait Payments {
  // All methods require 1 <= user && user <= 99999999.
  // Queries leave the abstract state unchanged.
  def incoming(user: Int): Int
  def outgoing(user: Int): Int

  // Require the corresponding old count < Int.MaxValue.
  // Increment only that user's named count by one.
  def recordIncoming(user: Int): Unit
  def recordOutgoing(user: Int): Unit
}
The preconditions and postconditions are part of the formal specification; the trait's type signatures alone cannot express all of them. The implementation below uses checked require calls for the relevant invalid operations.
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